Problem: Multiply the following complex numbers: $({-2}) \cdot ({-4+i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2}) \cdot ({-4+i}) = $ $ ({-2} \cdot {-4}) + ({-2} \cdot {1}i) + ({0}i \cdot {-4}) + ({0}i \cdot {1}i) $ Then simplify the terms: $ (8) + (-2i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 8 + (-2 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 8 + (-2 + 0)i - 0 $ The result is simplified: $ (8 - 0) + (-2i) = 8-2i $